Abstract
The gain of cellular motility via the epithelial-mesenchymal transition (EMT) is considered crucial in the metastatic cascade. Cells undergoing EMT to varying extents are launched into the bloodstream as single circulating tumor cells (CTCs) or multi-cellular clusters. The frequency and size distributions of these multi-cellular clusters has been recently measured, but the underlying mechanisms enabling these different modes of migration remain poorly understood. We present a biophysical model that couples the epithelial-mesenchymal phenotypic transition and cell migration to explain these different modes of cancer cell migration. With this reduced physical model, we identify a transition from individual migration to clustered cell migration that is regulated by the rate of EMT and the degree of cooperativity between cells during migration. This single cell to clustered migration transition can robustly recapitulate cluster size distributions observed experimentally across several cancer types, thus suggesting the existence of common features in the mechanisms of cell migration during metastasis. Furthermore, we identify three main mechanisms that can facilitate the formation and dissemination of large clusters: first, mechanisms that prevent a complete EMT and instead increase the population of hybrid Epithelial/Mesenchymal (E/M) cells; second, multiple intermediate E/M states that give rise to heterogeneous clusters formed by cells with different epithelial-mesenchymal traits; and third, non-cell-autonomous induction of EMT via cell-to-cell signaling that gives rise to spatial correlations among cells in a tissue. Overall, this biophysical model represents a first step toward bridging the gap between the molecular and biophysical understanding of EMT and various modes of cancer cell migration, and highlights that a complete EMT might not be required for metastasis.
Statement of significance The Epithelial-Mesenchymal Transition (EMT) confers motility and invasive traits to cancer cells. These cells can then enter the circulatory system both as single cells or as multi-cellular clusters to initiate metastases. We develop a biophysical model to investigate how EMT at the single cell level can give rise to a solitary or clustered cell migration. This model quantitatively reproduces cluster size distributions reported in human circulation and mouse models, therefore suggesting similar mechanisms in cancer cell migration across different cancer types. Moreover, we show that a partial EMT to a hybrid epithelial/mesenchymal cell state is sufficient to explain both single cell and clustered migration, therefore questioning the necessity of a complete EMT for cancer metastasis.
Introduction
Metastases are the leading cause of cancer-related deaths and still represent an insuperable clinical challenge (1). Typically, the epithelial cells in a primary tumor gain some degree of motility that enables migration through the adjacent tissues, invasion to breach the basement membrane and enter the bloodstream, and eventually colonize a distant organ to start a metastasis. Individually migrating cells - or circulating tumor cells (CTCs) - have been considered the primary drivers of metastasis. Recently, however, experimental evidence suggests that cells can also plunge into the bloodstream as multi-cellular clusters, which can more efficiently survive through the metastatic cascade and initiate a secondary tumor (2). In animal models, these clusters have been shown to initiate more than 95% of all metastases, despite accounting for as low as 3% of all CTC events (individual and clusters taken together) and typically only 5-8 cells large (3, 4).
The epithelial-mesenchymal transition (EMT) is commonly viewed as the mechanism that confers motility to epithelial cancer cells and enables migration (5, 6). EMT plays a crucial role during development and in physiological processes such as wound healing. During EMT, cells partially or completely lose E-cadherin-mediated adhesion junctions and apicobasal polarization while gaining motility and invasive traits (5). EMT is not a binary phenomenon; instead cells can display a spectrum of EMT states (7), including many hybrid epithelial/mesenchymal (E/M) cell states (8, 9). These hybrid E/M states can maintain some cell-cell adhesion typical of epithelial cells while acquiring the motility typical of mesenchymal cells, hence allowing collective migration leading to the formation of clusters of CTCs (7). So far, however, no quantitative model has been proposed to explain how a partial or complete EMT could potentially translate into the different frequencies and size distributions of CTC clusters observed in different tumors.
Here, we devise a biophysical model to investigate various modes of cancer cell migration enabled during a partial or complete EMT. In our model, cancer cells can undergo a complete EMT which allows solitary migration, but can also attain an intermediate, hybrid epithelial/mesenchymal (E/M) state that enables collective migration. These premises can explain the individual and clustered cell migration observed in different cancer types and robustly recapitulate the fraction and size distribution of CTC clusters experimentally observed in patients and mouse models, therefore offering a common framework for quantifying cell migration across different cancer types.
Furthermore, given the connection between hybrid epithelial/mesenchymal cell state(s), CTC clusters and poor prognosis (10), we seek mechanisms that increase the fraction of CTC clusters and allow the formation of larger clusters. First, a fast transition to a hybrid E/M state followed by a slow transition to a fully mesenchymal state can expand the fraction of hybrid E/M cells and facilitate the formation of large clusters. In the limiting case where cell can undergo only a partial EMT to a hybrid E/M state, but not a complete EMT, cells can still migrate in a solitary or collective fashion depending on the rate of EMT in the tumor tissue. Therefore, our model suggests that a partial EMT characterized by some conservation of an epithelial program might be sufficient to explain invasion in multiple cancers. Second, multiple intermediate hybrid E/M states facilitate the formation of large clusters and promote cell heterogeneity, mechanisms that can lead to higher plasticity, aggressiveness, and drug resistance (2). Third, cell-to-cell communication can propagate EMT induction signals and give rise to larger CTC clusters by enabling the induction of a hybrid E/M phenotype in a spatially coordinated way.
Methods
A percolation model with escape to couple epithelial-mesenchymal transition and cell migration
To investigate how the epithelial-mesenchymal transition (EMT) can give rise to different modes of cell migration, we develop a biophysical framework that couples the dynamic at a single cell and multi-cell levels. To model EMT, we consider a scenario where cells can assume one of three possible states: epithelial (E), hybrid epithelial/mesenchymal (H) and mesenchymal (M). In this setup, E cells have maximal adhesion with their neighboring cells and cannot migrate, while M cells do not have any adhesion with neighbors and can migrate solitarily. H cells have both adhesion and migration traits. Cells can switch from E to H state in partial EMT transitions and from H to M state in full EMT transitions with rate kEMT (Fig. 1A).
Second, to model cell migration, H and M cells can escape from the lattice and are then replaced by new E cells (Fig. 1B). This replacement represents the turnover of cancer cells, owing to their enhanced proliferation potential, that may also reach the periphery of the tumor. In fact, cells at the periphery of a tumor can be more exposed to EMT-inducing signals whereas cells in the interior exhibit more epithelial traits (11, 12).
M cells can only escape as single cells with a basal rate kESC, while H cells can escape either as single cells or as multi-cellular clusters. When two or more H cells are in contact, the cluster can escape as a whole or break into smaller subclusters (Fig. 1B). Therefore, H cells can migrate as single cells if they are not part of a cluster or in the limit case of a subcluster of only one cell. In general, the escape rate of a subcluster composed by m H-cells enclosed within a larger cluster composed by s H-cells is:
In this formula, c is a migration cooperativity index that describes how preferable it is for the H cells that compose the cluster to migrate together. In the limit case where c=0, there is no preference for collective migration. The case of c=1 implies a purely additive motility (i.e. a cluster of 2 H cells has twice the motility of a single H cell), while c>1 implies cooperation between H cells during migration (i.e. the motility of a 2-cell cluster is more than twice the motility of a single cell). Moreover, the cells in the cluster need to break the adhesive bonds with their neighbors in order to escape and migrate. These bonds are broken with probabilities PE (breaking of an E-H bond) and PH (breaking of an H-H bond). PE is always assumed to be smaller than PH because the E-H bond retains more adhesion as compared to the H-H bond. nE and nH are the number of nearest neighbor cells of the cluster in an E state and an H state, respectively, and in general depend on the dimension and connectivity of the considered lattice (see Supplementary figure 1A for an example on a 2D square lattice). In the case of a single mesenchymal (M) cell, m=1 and there are no adhesion bonds, therefore eq. (1) naturally relaxes to the basal escape rate kESC.
The rates of EMT and escape (kEMT, kESC) are the only timescales in the model. Therefore, we rescale time in units of 1/kESC so that the model is described by the dimensionless EMT rate k = kEMT/kESC while kESC = 1 in the new reference frame.
In a generic lattice with arbitrary dimension and connectivity, the flux of escaping clusters of H cells per unit time is quantified by considering every cluster in the lattice, every possible subcluster that could arise from any of those clusters, and the escape rate of any subcluster given by eq. 1. This approach, however, becomes computationally too expensive when considering large lattices. Therefore, we consider a mean-field approximation for the cluster flux:
In this expression, the first summation considers the probability to find clusters of a certain size s (ps(ρH)) for a certain fraction of H cells in the lattice (ρH). The second summation considers the relative frequencies (n(m, s)) and escape rates (K(m, s)) of subclusters of size m<s that could arise from a given cluster of size s.
The analytical expression of the cluster size distribution ps(ρH), however, is not known in any dimension D ≥ 2. Therefore, we consider cells arranged in an infinite one-dimensional chain. In this limit, ps(ρH) = ρHs(1 − ρH)2 from 1D percolation theory (13) and the relative frequencies of subclusters is n(m, s) = 2(s − m + 1)/[s(s + 1)] (Supplementary Information - A). To make the model more realistic from a biological standpoint (i.e. tumor tissues are not 1D structures), we consider an “effective-2D” approximation. In the effective-2D setting, the infinite 1D chain is in contact with two replicas that have the same fractions of E, H and M cells (Fig. 1C). This assumption reflects the fact that, in a 2D or 3D tissue, larger clusters have more nearest neighbors, and so more bonds to break to migrate (Supplementary Information-B). Compared to a 2D lattice model, the effective-2D approximation underestimates the migration of large clusters for two main reasons. First, for the same fraction of H cells in the chain (ρH), the probability to form large clusters is larger in a 2D lattice (supplementary figure 1B). Second, clusters in the effective-2D model are linear chains. Therefore, their number of nearest neighbors, and so the number of bonds to break, is maximized as compared to a 2D lattice (supplementary figure 1C).
The temporal dynamics of E, H, and M cell fractions (ρE, ρH, ρM) are described by ordinary differential equations that consider EMT transitions, escape of H and M cells, and replacement by new E cells:
Eqs. 3, along conservation of with cell fractions ρE + ρH + ρM = 1, provide the equilibrium cell fractions (ρE(eq), ρH(eq), ρM(eq)).
Results
The rate of EMT and cell cooperativity during migration give rise to a transition from single cell migration to cluster migration
First, we examine the steady state properties of the model as a function of the rate of EMT k. This parameter represents the ratio between the typical rate of EMT in a cancer cell and the typical rate of migration. Therefore, k ≪ 1 implies that cell migration is faster than EMT, while k ≫ 1 implies a fast EMT compared with cell migration.
In presence of a slow EMT (k ≪ 1), the lattice is mostly composed by epithelial (E) cells. Conversely, a maximal fraction of H cells is observed when the typical timescales for EMT and migration are similar (k ≈ 1). Finally, a very fast EMT (k ≫ 1) results in a largely mesenchymal (M) lattice (Fig. 2A). As a result, cell migration is predominantly solitary at low values of k (migration of individual H cells) and at large values of k (migration of individual M cells). Clustered cell migration is observed, although at a small fraction, for intermediate levels of k that enable a high fraction of H cells in the lattice (Fig. 2B).
Increasing cell cooperativity during migration, however, gives rise to a switch from single cell migration to clustered cell migration. Specifically, the fraction of escape events that involve clusters of any size larger or equal than 2 cells (Supplementary Information - C) increases as a combination of two factors. First, when the rate of EMT (k) is neither too high nor too low, ensuring a high fraction of hybrid H cells in the lattice; second, a high migration cooperativity (c) that promotes collective, rather than solitary, cell migration (Fig. 2C and supplementary figure 2A). Concurrently, parameters enabling a larger cluster escape fraction facilitate the formation of larger clusters, leading to an average cluster size of up to 5 cells (supplementary figure 2B). In fact, an intermediate rate of EMT (k) maximizes the fraction of H cells in the lattice, hence making the contact between two or more H cells more probable. Moreover, aggregates of H cells in the lattice tend to migrate together when the cooperativity (c) is high, hence forming larger clusters. These trends observed in cluster escape fraction and size are robust upon local and global variation of the model’s parameters (supplementary figure 2C-D).
This variability in the frequency of CTC clusters is well-supported by multiple independent experiments that reported variable fractions of CTC clusters in circulation (3, 14–18). These CTC cluster fractions indicate that different cancer types are characterized by different migratory regimes, that in turn correspond to different combinations of EMT rate and cooperativity (k, c) in the model (supplementary figure 3). Potentially, different cancer subtypes or even patient-specific factors might further increase this variability. Supporting the prediction of the effective-2D modeling framework, a similar single cell-cluster transition can be observed in both a 1D linear chain and in a square, two-dimensional lattice (supplementary figure 4).
The single cell-cluster migration transition recapitulates cluster size distributions across several cancer types
We further investigate how the transition from individual migration to cluster-based migration is reflected in an increased probability to observe larger clusters by calculating the escape probability of clusters with different sizes (Supplementary Information - C).
First, for an intermediate rate of EMT (k) and low migration cooperativity (c), the cluster size distribution is steep and mostly dominated by single cells (i.e. no clusters). Increasing the cooperativity at a fixed EMT rate, however, modifies the shape of the distribution such that clustered cell migration becomes the primary migration mode (supplementary figure 5A). Additionally, for a high level of cooperativity, the cluster size distribution is steep for extreme values of k, while cluster cell migration is supported at intermediate levels of k (supplementary figure 5B).
Such variability can quantitatively capture cluster size distributions observed in different cancer types. First, data from melanoma patients acquired via microfluidic trap (19) shows a very steep distribution where large clusters are rare. This scenario is reproduced well by a model with low cooperativity (c=3) (Fig. 3A). Similarly, a cluster size distribution from prostate cancer (14) shares similar traits but slightly larger tail, and maps well on to a larger cooperativity index (c=4) (Fig. 3B). Microfluidic data of breast cancer patients (19) shows a more prominent role of large clusters, where approximately two-thirds of the observed clusters are composed by more than two cells. Such scenario is better recapitulated by a model with increased cooperativity (c=5.5) (Fig. 3C). For these three datasets, the frequency of single cells was not reported due to technical limitations. Our model predicts that single cell migration is the prevalent migration mode in these three cases, with a fraction of 92%, 84% and 55% of single CTCs, respectively (supplementary table 1). A mouse model of breast cancer shows a broad distribution with large clusters of 6-8 cells (Fig. 3D). While the model can qualitatively capture the transition toward a more clustered migration with a higher cooperativity (c=6), the probability to observe clusters remains relatively constant within a certain range of size in the experimental dataset (Fig. 3D). A further increase of cell cooperativity, however, gives rise to a different regime where small clusters become more probable than single cells (c=8.5, Fig. 3E). The onset of this single cell-cluster transition recapitulates well the size distribution measured in a mouse model of myeloma (20) that peaks for a cluster size of n=4 cells (Fig. 3E). In this case, single cells and small clusters of n=2 cells could not be measured experimentally, but our model predicts those to account approximately for only 3% and 8% of the total CTC fraction, while larger clusters of 3-5 cells account for about 68% of the total CTC fraction (supplementary table 1). CTC clusters detected in human glioblastoma (21) (Fig. 3F) are mapped onto an even higher cooperativity (c=9). Similar to the case of breast cancer (Fig. 3D), our model qualitatively captures the shape of the distribution but underestimates the frequency of large clusters composed by 7-8 or more cells in the case of glioblastoma (Fig. 3F). Finally, another mouse model of breast cancer (4) is characterized by a typical cluster size of 5-10 cells, and is largely devoid of individual CTCs and smaller CTC clusters. This size distribution can be mapped onto a very high cooperativity index (c=10) without increasing the rate of EMT (Fig. 3G). Thus, an increased value of the cooperativity parameter (c), without any further increase in rate of EMT, can account for the larger sized CTC clusters isolated from circulation. Indeed, at least some breast cancer cells have been proposed to invade collectively through a conserved epithelial program (22, 23).
The abovementioned datasets have been reproduced with a fixed EMT rate and increasing cooperativity. However, this is not the only combination in the two-dimensional parameter space of (c,k) that can reproduce these experimentally observed distributions. Indeed, several combinations of the EMT rate and cooperativity can quantitatively reproduce these distributions (supplementary figure 5C-I). In summary, a progressing tumor can access the cluster-based dissemination mode by (i) increasing the migration cooperativity at fixed EMT rate, (ii) increasing/decreasing its EMT rate from an extreme value and large enough cooperativity, or (iii) with a combination of these two pathways. (Fig. 3H).
A model of only partial, and not complete EMT, can explain both single cell and cluster migration
The biophysical model of EMT with 3 cell states (E, H, M) could not quantitatively capture (i) broad distributions where clusters of different sizes have similar frequencies (see Fig. 3D, 3F) and (ii) the presence of large CTC clusters of more than 8-10 cells in tumors characterized by collective migration (see Fig. 3F-G). Different molecular mechanisms, however, can interfere with the multiple steps of EMT, stabilize hybrid epithelial/mesenchymal phenotype(s) and give rise to more CTC clusters (25–28) by either (i) facilitating the transition from E to H, or (ii) preventing the transition from H to M. To address this scenario, we separately consider a rate of partial EMT that regulates the transition from epithelial (E) to hybrid (H) and a rate of complete EMT that regulates the transition from hybrid (H) to mesenchymal (M) (Supplementary Information - D).
The interplay of timescales for partial and complete EMT regulates the composition of the tumor tissue. As expected, a fast partial EMT, coupled with a slow complete EMT, generates a high fraction of hybrid E/M cells in the lattice (Fig. 4A). A slow partial EMT, however, results in an epithelial lattice, while the tissue is mostly mesenchymal when both the processes are fast (supplementary figure 6A-B). Therefore, an increased rate of complete EMT (kComplete EMT) does not favor a large fraction of cells disseminating as clusters (supplementary figure 6C). Indeed, a high expression of ‘phenotypic stability factors’ that can stabilize hybrid epithelial/mesenchymal phenotype(s) and increase the mean residence times in these phenotypes by preventing them from undergoing a complete EMT (i.e. reduce kComplete EMT effectively) have been correlated with higher aggressiveness and worse patient survival in multiple cancer datasets (26–29), corroborating the evidence of clusters being the primary ‘bad actors’ of metastasis. In the limit where the rate of progression to a complete EMT state is very slow (kComplete EMT ≪ kPartial EMT), the model is restricted to the epithelial state and the hybrid state (Fig. 4B). In this 2-state limit, the model reaches a fraction of H cells very close to 1 for larger enough kPartial EMT (Fig. 4C). In this situation, the lattice undergoes percolation of H cells, and the level of cooperation during migration distinguishes between a solitary or a collective migration. Without cooperativity, only single cells and small clusters are observed, while a higher cooperativity gives rise to larger clusters (Fig. 4D). Strikingly, this 2-state model reproduces effectively the experimental CTC cluster size distributions characterized by a more collective migration. Compared to the 3-state model considered earlier (Fig. 3), the 2-state model can correctly captures the broad size distributions observed in breast cancer and glioblastoma (21, 24) (Fig. 4E-F) and the collective invasion with large clusters >10 cells reported in breast cancer (4) (Fig. 4G). This picture is consistent with the fact that, at least in breast cancer, a conserved epithelial program, rather than a complete EMT, is required for collective invasion (22).
These results suggest that a partial EMT to a hybrid epithelial/mesenchymal state can be sufficient to explain the different regimes of solitary and collective migration observed across different cancers, and therefore that single cell migration via a complete EMT might not be essential for metastasis.
Multiple intermediate hybrid states facilitate cluster dissemination and heterogeneity
Recent experiments suggest that multiple hybrid states with mixed epithelial and mesenchymal traits can exist with distinct epigenetic landscapes and morphological features (30–32).
Therefore, we generalize the model to an arbitrary number n of intermediate hybrid states. It is assumed that an epithelial cell transitions through the n intermediates in an ordered fashion to become mesenchymal. Furthermore, the intermediate states are orderly ranked, and every transition (Hi → Hi+1) makes the cell less epithelial and more mesenchymal, i.e. cells in more advanced intermediates are increasingly less adhesive and have an increasingly higher probability to break the bonds with their neighbors. A different scenario, not considered here, would envision multiple parallel pathways from E to M that pass through different intermediate states. In the model, cells in different intermediate states can migrate together as clusters (Supplementary Information - E).
Increasing the number of intermediate states results in a larger cluster escape fraction and makes more probable, by orders of magnitude, to observe rare events of large clusters (Fig. 5A-B). Moreover, multiple intermediate states enable cluster-based dissemination with a higher fraction of CTC clusters at a much lower cooperativity index, compared with the case of only one intermediate state (supplementary figure 7A).
Moreover, multiple intermediate states result in a more heterogeneous cluster composition. Specifically, in a case with three intermediate states (H1, H2, H3), clusters are composed by cells that are more epithelial-like (E-like or H1), epithelial/mesenchymal-like (E/M or H2), and mesenchymal-like (M-like or H3). This heterogeneity has been well-reported in both clusters cultivated in vitro and circulating tumor clusters in vivo, where staining revealed that (i) only certain cells in the cluster express epithelial or mesenchymal markers and (ii) certain cells robustly express both epithelial and mesenchymal markers (3, 33–35). Similarly, multiple intermediate states give rise to a spectrum of single migrating cells with different EMT traits (Fig. 5D). If EMT is slower than the cell migration (kEMT ≪ 1), most cells migrate as soon as they transition to an E-like state. Therefore, in this case, most of the migrating cells lean toward the epithelial end of the EMT spectrum (Fig. 5D, left region). Conversely, for a faster EMT (kEMT~1), most migrating cells lean toward the mesenchymal end of the EMT spectrum (Fig. 5D, right region). The heterogeneity of cluster composition and single cell states is conserved even for higher levels of migration cooperativity. While the fraction of single migrating cells decreases for higher c, single migrating cells are still observed in E-like, E/M, and M-like states. (supplementary figure 7B-C). This heterogeneity in cell migration has been well reported experimentally, and could be informative of the tumor progression and response to treatments. We compared the model’s predictions with the CTC cell fractions measured in the bloodstream of breast cancer patients (36) (Supplementary Information - F). Notably, patients that responded positively to treatment maps onto smaller EMT rate (k) in the model after treatment, while patients that underwent tumor progression maps onto a larger EMT rate after treatment (supplementary figure 8).
Cell-to-cell EMT induction creates larger clusters and gives rise to spatial correlations among cells
EMT is not necessarily a cell autonomous process. Cell-to-cell signaling can additionally regulate EMT through multiple mechanisms, including contact-based ligand-receptor interactions and secretion of exosomes (5).
Therefore, we consider a scenario where cells in a partial EMT state can, in turn, induce EMT in neighboring cells. We assume, however, that this contact-based EMT induction requires adhesion between neighboring cells. For this reason, M cells cannot induce EMT in neighbors because, although they have an active EMT program, they have no residual cell adhesion. Similarly, an E cell will receive a stronger EMT induction from its neighbor H cells as compared to another H cell, because the adhesion of an E-H bond is greater. Therefore, in addition to the cell autonomous EMT rate (k), we introduce a noncell autonomous EMT term that depends on a basal cell-to-cell signaling rate (kCell-Cell) and the number of neighboring H cells that a cell has (Supplementary Information - G).
Increasing the noncell autonomous EMT rate (kCell-Cell) generates a higher fraction of escaping clusters (Fig. 6A) and larger clusters (supplementary figure 9). Interestingly, if either k or kCell-Cell are larger than 1 (the typical timescale for escape in the model), the fraction of clusters decreases because the fast EMT rate gives rise to a high fraction of M cells that migrate in a solitary fashion.
Furthermore, cell-to-cell EMT induction gives rise to spatial correlations among H cells. This correlation can be quantified by the average number of H neighbors that a H cell has (nH). In a linear chain, each cell has two nearest neighbors that are hybrid (H) with a probability equal to the fraction of H cells in the lattice (ρH). Therefore, on average, each H cell is expected to have nH = 2ρH hybrid H nearest neighbors in the absence of correlations. In the case of strong cell-to-cell EMT induction, however, nH becomes significantly larger than 2ρH because H cells tend to be in contact rather than stochastically scattered, and the correlation index (nH − 2ρH)/2ρH becomes positive (Fig. 6B).
A direct comparison shows a slight anti-correlation when kCell-Cell < k because H-H cell contacts can be lost via cell migration. The correlation is maximal when kCell-Cell is similar to the escape rate (kESC = 1) and decreases when kCell-Cell is significantly larger (Fig. 6C). Confirming the notion that intermediate levels of kCell-Cell maximize the correlation among H cells, the probability distribution of cluster escape as a function of cluster size has a larger tail for kCell-Cell = 1 and is steeper for extremal values of kCell-Cell (Fig. 6D).
These results show that cell-to-cell signaling is crucial to enable the formation of large clusters of H cells from a single EMT event by propagating EMT from neighbor to neighbor (Fig. 6E).
Discussion
Are there common traits in the migration of cancer cells?
We propose a model that couples the epithelial-mesenchymal phenotypic transition at a single-cell level with cell migration. In the model, mesenchymal cells that have undergone a complete EMT can only migrate as single cells, while cells midway en route to EMT, or hybrid epithelial/mesenchymal (E/M), can either migrate as single cells or as multi-cellular clusters. The model predicts a transition from a migratory regime mostly dominated by single mesenchymal cells to a regime mostly dominated by hybrid E/M cell clusters. This transition depends on the rate at which cells undergo EMT and on the level of cooperativity that quantifies how probable it is for hybrid E/M cells to migrate together rather than as single cells. This simple physical model can quantitatively reproduce different cluster size distributions observed in the bloodstream of patients and/or in experimental mouse models. These experimental datasets exhibit a tremendous variability, ranging from cases where large clusters are highly improbable to cases of collective migration (4, 14, 19–21, 24), all of which can be captured by the model for varying parameter combinations.
Nonetheless, there are multiple limitations to our model. First, cancer cells in a tumor tissue can proliferate, hence introducing an additional modulation to cell patterning. Second, we do not consider the death of CTCs in circulation, which may depend on the cluster size (37). Third, additional mechanisms of aggregation can modulate the size of these clusters after detachment from the primary tumor, such as collisions in the bloodstream (38). Fourth, the CTC clusters may contain non-cancerous cells such as neutrophils (39). Finally, it is worth pointing out that the abovementioned datasets have been acquired in different systems and with different experimental techniques, which might have affected the accuracy in detection of CTC clusters. With these caveats being raised, these results support the idea that multiple aspects of cancer cell migration are highly conserved across cancer types, and microenvironmental, case-specific factors might set the conditions for a more individual or collective migration by regulating cancer cell heterogeneity in terms of EMT and migration, as effectively represented by the variation of the parameters in the model. Supporting this picture, it has been recently shown that multiple breast cancer cell lines with varying origin and morphological features can switch from solitary to collective migration by manipulating the physical properties of the extracellular medium in vitro (40, 41).
Is a complete EMT necessary for cancer metastases?
Cell invasion during the metastatic cascade can operate via multiple mechanisms, such as single cell invasion upon activation of a ‘full EMT’ program or collective invasion characterized by a basal-like phenotype that conserves E-cadherin contacts between cells (22, 42). EMT, at least in the cancer metastasis field, has been largely viewed as a binary process – no migration (no EMT) or individual migration (full EMT) – but recent evidence has suggested that EMT need not be an ‘all-or-none’ linear unidimensional process (43). The existence of one or more hybrid epithelial/mesenchymal states capable to invade while maintaining cell-cell adhesion has been proposed as a possible explanation for the different modes of invasion (43). Supporting this hypothesis, hybrid epithelial/mesenchymal phenotype(s) have been associated with stemness and tumor-initiation ability (31, 44–47), while inducing a complete EMT has been shown to even restrict tumor aggressiveness and metastatic potential in some cases (48–51). Here, we show that a model of only partial EMT that can be associated with a partially conserved epithelial program can still give rise to different regimes characterized by more individual or more collective cell migration. While a model of complete EMT could correctly recapitulate the size distribution of CTC clusters in contexts where the migration is mostly solitary, a model of only partial EMT could quantitatively reproduce cases of both solitary and collective migration. These observations suggest that, although a complete EMT can take place in certain types of cancer, a partial EMT might be sufficient to explain the different modes of invasion, and seems necessary for collective migration. Therefore, this model identifies hybrid E/M state(s) as a potent concept to unify qualitatively different modes of cancer cell migration. A similar variety of migratory modes is observed in the field of developmental biology, where the idea that a complete EMT and collective migration represent extreme instances of a larger spectrum of behaviors is gaining traction as well (52).
What molecular mechanisms can maximize the metastatic potential of CTC clusters?
First, we show that multiple, instead of a single, hybrid E/M state give rise to heterogeneous clusters composed by cells with different states along the EMT spectrum. This heterogeneity might enable co-operation among different phenotypes in executing various aspects of metastasis, hence increasing the survival probability of clusters in circulation. For instance, completely mesenchymal CTCs are associated with a more favorable survival outcome in breast cancer (53), and completely mesenchymal cells lose their metastatic potential in squamous cell carcinoma (54). Moreover, cell-to-cell communication can regulate the patterning of cells with different EMT phenotypes, and EMT induction between neighboring cells can rapidly give rise to large E/M clusters. In this regard, molecules of the Jagged family that promote cell-to-cell signaling are considered promising therapeutic targets (55). The exchange of Jagged ligands that bind through the Notch receptor facilitates bi-directional cross-talk between cells, stabilizes hybrid E/M cell phenotype(s) and promotes resistance to therapies (55–57). Previous efforts to couple EMT with intercellular signaling have disregarded the loss of cell-cell adhesion leading to a reduced cell-to-cell signaling between mesenchymal cells (58). Also, we recently showed that JAG1, a Jagged ligand subtype, promotes the growth of tumor organoids in breast cancer cells in vitro (12). Overall, these observations suggest that Jagged can facilitate a ‘plasticity window’ that maximizes tumor aggressiveness in terms of EMT, proliferation and therapeutic resistance (45). Consistently, CTC clusters exhibit higher levels of JAG1 as compared to single CTCs in breast cancer (4, 23).
Conclusions
Overall, the emerging picture suggests similar mechanisms to acquire motility and invasive traits, which might be regulated differently in different cancers, hence leading to different modes of migration. Our model suggests that tumors that are more mesenchymal tend to disseminate more in the form of single CTCs and only rare clusters, while tumors where EMT is more tightly regulated and are more hybrid E/M (intended, generally, as either one or a spectrum of states with mixed epithelial-mesenchymal traits) may disseminate as clusters more efficiently (Fig. 7). Thus, counterintuitive to the long-standing paradigm, mechanisms that inhibit a complete EMT and instead stabilize hybrid E/M state(s) might bear a higher metastatic potential (27, 28, 59). Future investigations should therefore focus on identifying the molecular mechanisms that drive a progression to a mesenchymal state or maintain a partial EMT instead.
Cell migration appears ubiquitously in a multitude of physiological and pathological contexts, and it has been the subject of several theoretical and computational investigations. Most of these efforts, however, have been devoted toward understanding either the molecular mechanisms that enable such transition within a single cell (60, 61) or the different invasive modes that arise from the mechanical properties of cells (62, 63). This work offers a first step toward an integrated understanding of cell migration and its underlying signaling mechanisms. Future efforts will further investigate the coupling between the signaling and mechanical aspects of cancer cell migration en route to a better understanding of cancer metastasis.
Author contribution
FB developed the model, produced the results and wrote the manuscript; MKJ and JNO supervised the research. All authors discussed the results and edited the manuscript.
Acknowledgements
The authors thank Prof. Herbert Levine (Northeastern University) for his valuable suggestions. The work in the Onuchic Lab was supported by the Center for Theoretical Biological Physics (NSF PHY-1427654). Federico Bocci was supported by the Marjory Meyer Hasselmann Fellowship. Mohit Kumar Jolly was supported by Ramanujan Fellowship provided by SERB, DST, Government of India (SB/S2/RJN-049/2018).
Footnotes
Some corrections in the results and methods section, as well as title change.